Particle Dynamics in Very Strong Electromagnetic Fields

The still unsolved problem of the origin of ultra high en-ergy cosmic radiation and related phenomena of individual and collective particle motion in extremly strong electro-magnetic fields associated with compact objects [l] have renewed the interest in radiation and radiation reaction as described within the frames of Mazwell theory. Unfortunately, as is well known, the classical equation of motion ’ based on the early work of H.A. Lorentz [2], M. Abraham[3, 4] and M. I;aue [5, 61 also describes un-physical run-away solutions which have been widely dis-cussed in literature. In principal, these can be avoided by appropriate initial conditions. But then the question of stability of solutions arises. Various attempts have been published since then to de-duce stringently the correct equation of motion. Quit